R.E. Richards

The signal-to-noise ratio of the nuclear magnetic resonance experiment

Abstract A fresh approach to the calculation of signal-to-noise ratio, using the Principle of Reciprocity, is formulated. The method is shown, for a solenoidal receiving coil, to give the same results as the traditional method of calculation, but its advantage lies in its ability to predict the ratio for other coil configurations. Particular attention is paid to the poor performance of a saddle-shaped (or Helmholtz) coil. Some of the practical problems involved are also discussed, including the error of matching the probe to the input impedance of the preamplifier.

Critical factors in the design of sensitive high resolution nuclear magnetic resonance spectrometers

An analysis is given of the factors which influence the performance of a Fourier transform n.m.r. spectrometer including field homogeneity, probe design, transient circuit behaviour, Johnson noise, non linear analysis, phase sensitive detection in quadrature, and signal processing. The building of a spectrometer based upon the analysis of these factors is described, as is the use of a cyclically ordered phase sequence (CYCLOPS) which renders the use of quadrature Fourier transformation easy. Theoretical deductions are experimentally verified, and the performance of the instrument is demonstrated with spectra obtained from caesium and phosphorus resonances.

Application of 31P NMR to model and biological membrane systems.

Proton, deuterium and carbon magnetic resonance techniques have been widely used to study the hydrocarbon chain region of model bilayer systems and biological membranes (for a review see [l]). More recently, phosphorus magnetic resonance (31P NMR) has been introduced to study the polar headgroup region of membranes [2-71. In this communication we show how 31P NMR can define an order parameter for the phosphate headgroup in model and biological membranes. In addition, in oriented systems the 31P NMR spectrum can provide information on the orientation of the membrane.

Factors affecting the motion of the polar headgroup in phospholipid bilayers. A 31P NMR study of unsonicated phosphatidylcholine liposomes

(1) The 129 MHZ and 36.4 MHZ 31 P NMR spectra of unsonicated liposomes consisting of phosphatidylcholines of varying chain length and unsaturation have been investigated. (2) In the liquid crystalline state the 31 P NMR liposome spectra are similar for both saturated and unsaturated phosphatidylcholines, demonstrating that the motion of the polar headgroup is not sensitive to the fatty acid composition in the disordered liquid crystalline state. (3) Below the hydrocarbon phase transition temperature there is a marked increase in the linewidth of the 31P NMR liposome spectra, indicating a reduction in the motion of the polar headgroup. (4) The addition of equimolar concentrations of cholesterol to phosphatidylcholine eliminates phase transition effects experienced by the polar headgroup. The motion of the polar headgroup is then very similar to that obtained in the liquid crystalline state for pure phosphatidylcholine bilayers. (5) In the liquid crystalline state the motion of the polar headgroup in the phosphate region is insensitive to changes in the available area per phosphatidy-choline molecule.

Cobalt Nuclear Resonance Spectra

The frequencies of the cobalt nuclear resonances of solutions of fourteen cobalt (III) complexes have been measured in a magnetic field of 4370.9G. The temperature coefficient of the nuclear resonance frequency of two of the complexes has been measured, and the effect of variation of solvent studied. The electronic absorption spectra of the complexes have also been measured, and the absorption band shifts which occur when the temperature is changed have been studied for two of the complexes. The nuclear resonance frequencies show a close correlation with the spectrochemical series of the ligands. Following a suggestion by Orgel, a simple interpretation of the chemical shifts is developed in terms of crystal field theory. The theory predicts a linear relation between the cobalt nuclear resonance frequency and the wavelength of the lowest frequency optical absorption maximum of the octahedral complexes. The compounds studied support this prediction. Using measured values of the temperature coefficient of the nuclear resonance frequency and the optical absorption wavelength, the theory permits the temperature dependence of the optical spectrum to be calculated. In the two cases studied the calculations are in satisfactory agreement with experiment. The results provide information about the ‘electronic shielding’ of the cobalt nucleus which leads to an improved value of the cobalt nuclear moment.

Frequency dependence of 31P NMR linewidths in sonicated phospholipid vesicles: Effects of chemical shift anisotropy

Phosphorus nuclear magnetic resonance (3’P NMR) is an increasingly important physical technique for the elucidation of structural features of phospholipid bilayer membranes [l-S] . In sonicated vesicles, however, the chemical shift differences between different classes of phospholipids are of approximately the same magnitude as the widths of the resonances themselves [5,6]. For many applications it is desirable to find conditions which optimize the resolution of these signals. In general, the resolution of chemically-shifted resonances is improved by increasing the field strength, as the separation of the resonances increases linearly with the field strength, while the width of the resonances is usually field-independent. The 31 P NMR spectrum from unsonicated phospholipid dispersions is, however, dominated by the chemical shift anisotropy of the phosphate group [2,4]. It might therefore be expected that the 31P NMR linewidths in the sonicated phospholipid bilayer systems would contain a term which arises from the modulation of this chemical shift anisotropy by the isotropic tumbling of the vesicles. In this case, the 31P NMR linewidths of sonicated bilayer vesicles would broaden as the

31P NMR of Phospholipid membranes: Effects of chemical and anisotropy at high magnetic field strengths

Abstract The 31 P NMR spectrum of sonicated dipalmitoyl lecithin vesicles consists of two chemically shifted resonances, separated by ∼0.15 ppm, which arise from phosphate groups in phospholipid molecules on the inside and the outside of the spherical bilayer vesicles. The widths of the resonances are remarkably sensitive to the crystalline-liquid crystalline phase transition, the magnetic field-strength, and the viscosity of the surrounding aqueous medium. The results are interpreted in terms of two phosphorus relaxation mechanisms: modulation of the anisotropic phosphorus chemical shift and dipolar interaction with protons on adjacent methylene groups. At high magnetic fields (7.5 T) the modulation of the phosphorus chemical shift anisotropy by the Brownian rotation of the intact spherical vesicles dominates the linewidth. The chemical shift anisotropy in the sonicated vesicles is compared with that in the unsonicated dispersions. It is concluded that the structure around the phosphate group is not significantly disrupted by the sonication process. The order parameter for the internal motion of the phosphate group is estimated, and a tentative model for the motion of the phosphate group in the membrane is proposed.

Nuclear electron double resonance in liquids

In this contribution we hope to illustrate with preliminary measurements some of the ways in which nuclear-electron double resonance experiments can yield information of value to the chemist. The magnetic coupling between a paramagnetic electron of spin S and a nucleus of spin I may be described (Abragam 1961) by the spin Hamiltonian Hs, I = γeγn I [3r(S. r)/ r 5 – S/ r 3 + 16 π /3 S| ψ e (0)|2], where γe, γn are the electron and nuclear gyromagnetic ratios respectively, r is the vector radius joining I and S and | ψe (0)|2 is a measure of the overlap between the electron and nuclear wave functions. The first two terms describe the magnetic dipole-dipole interaction dominant at large interspin distances, and the third covers any short-range scalar or contact interactions. In non-viscous solutions of free radicals the rapid relative motion of the spins causes the Hamiltonian to become time dependent. If the motion is quite random the dipolar terms become entirely time dependent and are significant only in electron-nucleus relaxation phenomena. The scalar term, on the other hand, may not be completely averaged and can thus cause both relaxation phenomena and paramagnetic shifts in the nuclear resonance spectrum of the solvent (Bloembergen 1957). Thus the dynamic parts of both the scalar and the dipolar interactions are effective in producing mutual relaxation of the spins. Just which of the possible two spin processes is the most effective can be found by expanding the time-dependent Hamiltonian from equation (1) into its component spin operators and finding their relative spectral densities (Abragam 1955,1961). The dipole-dipole part of the Hamiltonian then becomes H d.d( t ) = [ J 1 SzIz + J 2{S+I_ + S_I+} + J 3{ S z I+ + I z S+} ( A ) ( B ) ( C ) + J 3{ S z I_ + I z S_} + J 4{S+I+} + J 4 {S\_I\_}] σ1/ , ( D ) ( E ) ( F ) and the scalar part becomes H sc. ( t ) = [ J 5 S z I z + J 6{S+I_ + S_I+}] σ2| ψe (0)|2, where is the mean value of the cube of the electron-nuclear distance, σ1 and σ2 are proportionality constants, the J ’s are the spectral densities, S z , Iz are the z components of the spin operators and S+I+; S\_I\_ are the raising and lowering operators for the electron and nuclear spins respectively. For a white spectrum of relative motions between the spins, terms E and F are not the most important for dipolar coupling. This leads to the established reversal of nuclear polarization in Overhauser experiments between nuclei with positive magnetic moments and electrons (Richards & White 1962 a, b ). Under the same conditions a dominant scalar coupling leads to an enhancement of the nuclear polarization because of its different relaxation operators.

Phosphorus nuclear magnetic resonance in phospholipid dispersions.

Abstract The 31 P nuclear magnetic relaxation times ( T 1 and T 2 ) were determined for several lipid—water phases. By comparison of the results for different lipids, and by observation of the changes in T 2 which occur at the transition temperature for dipalmitoyl lecithin, it is concluded that the relaxation times reflect the mobility of the lipid head group.

Nuclear electron double resonance and scalar interactions in solutions

The electron-nuclear Overhauser effect at two magnetic fields has been investigated for solutions of 2, 4, 6-tri-tert. -butyl phenoxy radical in several protonated and fluorinated organic solvents. In some cases the enhancement of the nuclear resonance is positive in sign, and the results have been interpreted in terms of the theory of Hubbard (1966) in which both dipolar and scalar interactions between the electrons and nuclei are considered. Hubbard assumes two models for the scalar interaction which he calls the sticking and diffusion models. The experimental results may be best explained in terms of the diffusion model. The theory permits calculation of the diffusional correlation times, distances of closest approach of the nuclei to the electrons, and relative diffusion coefficients of the solvent and radical molecules. Reasonable values are obtained for the systems investigated.